Critical point of tori collision in quasiperiodically forced systems

We report on a type of scaling behavior in quasiperiodically forced systems. On the parameter plane the critical point appears as a terminal point of the tori-collision bifurcation curve; its location is found numerically with high precision for two basic models, the forced supercritical circle map and the forced quadratic map. The hypothesis of universality, based on renormalization group arguments, is advanced to explain the observed scaling properties for the critical attractor and for the parameter plane arrangement in the neighborhood of the criticality.

Experimental observation of dynamics near the torus-doubling terminal critical point

A nonlinear electronic circuit driven by two signals with golden mean frequency ratio is studied. We have observed different dynamical regimes, including tori, doubled tori, strange nonchaotic attractors, and chaos, which all meet together at the critical point terminating the torus-doubling bifurcation curve (TDT point) in the parameter plane of the system. The parameter plane arrangement, spectra, and portraits of attractors observed in the experiment are in reasonable coincidence with numerical computations for a quasiperiodically forced logistic map, where the TDT critical point originally has been found and studied theoretically [S. Kuznetsov, A. Pikovsky, and U. Feudel, Phys. Rev. E 57, 1585 (1998)].